Symmetry relations of two-dimensional photonic crystal cavity modes

Degeneracy of resonant modes in two-dimensional (2-D) photonic crystal cavities are investigated using the symmetry relations. The 2-D photonic crystal cavity tends to have either a pair of doubly degenerate modes or nondegenerate modes. We derive simple relations between degenerate modes without using a rigorous group theory. These relations are useful for classifying the resonant modes into degenerate pairs and nondegenerate ones.